3 votes 3 votes In a system an RSA algorithm with $p=5$ and $q=11$, is implemented for data security. What is the value of the decryption key if the value of the encryption key is $27?$ $3$ $7$ $27$ $40$ Computer Networks isro2014 computer-networks network-security + – ajit asked Sep 23, 2015 • edited Dec 4, 2022 by Lakshman Bhaiya ajit 6.2k views answer comment Share Follow See 1 comment See all 1 1 comment reply alekhya commented Jun 2, 2016 reply Follow Share but (3+27)%40=30 so how could be the ans as option (a). Please explain that. 0 votes 0 votes Please log in or register to add a comment.
Best answer 15 votes 15 votes RSA Algorithm http://courses.cs.vt.edu/~cs5204/fall00/protection/rsa.html and example https://www.cs.utexas.edu/~mitra/honors/soln.ht Answer of above , p=5 , q=11 , encryption key(e) = 27 n = p*q = 5*11= 55 φ(n) = (p - 1) * (q - 1) = 4 * 10 = 40 Given[e = 27], d such that (d * e) % φ(n) = 1 decryption key (d) --> (d * 27) % 40 = 1 so , when d =3 than L.H.S = R.H.S Answer option (a). Vinay Yadav answered Sep 23, 2015 • selected Feb 6, 2017 by Prajwal Bhat Vinay Yadav comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes n = 5 * 11 = 55 ∅(n) = (p-1)(q-1) = 40 e = 27, d = ? ed mod( ∅(n) ) = 1 27d mod 40 = 1 try all option for d, let, d=3 ------- (27*3)mod40 = 81 mod 40 = 1 option A the answer rameshbabu answered Jun 29, 2016 rameshbabu comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Answer: (a) Explanation: RSA algorithm is is an asymmetric cryptographic algorithm. RSA involves a public key (encryption key) and private key (decryption key). Choose two different large random prime numbers p and q. Here already given p = 5, q =11. Calculate n = p*q where n is the modulus for the public key and the private keys. Here n = 55. Calculate the totient: ϕ = (p − 1) * (q − 1). Here ϕ = 40. Choose an encryption key integer e such that 1 < e < ϕ and e is co-prime to ϕ i.e. e and ϕ share no factors other than 1 or we can say gcd(e, ϕ) = 1. Here e is already given that is e = 27. Compute an decryption key d to satisfy the congruence relation d * e ≡ 1 mod ϕ. Here we require to find out the value of decryption key.d * 27 = 1 mod 40 => d = 81 Reference: https://simple.wikipedia.org/wiki/RSA_(algorithm) Mangilal Saraswat answered Jun 26, 2016 Mangilal Saraswat comment Share Follow See all 0 reply Please log in or register to add a comment.